Could an organism be both MR and V-P positive? Could an organism be fermenter and also be both MR and V-P neg?

Answers:
Yes for the first question--this is possible! I believe that a certain enteric organism (Proteus mirabilis, if I'm not mistaken) utilizes both fermentative pathway, although I won't be surprised if another organism from a different genus can do this as all right.

For the second question, yes, explicitly possible. I say so because some fermenters CAN utilize their extremity products even after producing them in solution. I believe that you take in that the end products of both methyl-red and Voges-Proskauer test are organic acids, which are detected by pH indicators contained by solution. Now, imagine if a fermenter uses up the life acid within the broth, making the medium neutral--this creates a false gloomy result even though they are actually positive, and here are fermenters that do this although I can't name them at the top of my chief.

In essence, they SHOULD be positive, although one will always find an exception to the rule IF one designs the great experiment to determine if the negative result is indeed glum or just a false result.